Conventionally, there is disclosed a technique in which a catalyst for purifying exhaust gas is installed in an exhaust pipe of an internal combustion engine. In order to activate the catalyst at an early stage immediately after the start of the internal combustion engine, a fuel injection amount is increased/decreased for every combustion, and an air-fuel ratio is oscillated between a rich side and a lean side with respect to the stoichiometric air-fuel ratio (for example, see JP-A-4-308311). That is, the air-fuel ratio is oscillated between the rich side and the lean side, so that rich combustion and lean combustion are repeated, the temperature of the catalyst is raised by oxidation reaction heat generated at that time, and the early activation of the catalyst is accelerated.
In this case, the amplitude amount of the air-fuel ratio has been determined by trial and error at the time of adjusting the internal combustion engine in view of variations of drivability due to a change in driving environment and a change in operation state of auxiliary equipment of the internal combustion engine.
However, in the existing device, since the air-fuel ratio is oscillated with the amplitude amount previously determined by the adjustment, even in the case where there is room for the amplitude of the air-fuel ratio according to the driving state of the internal combustion engine, the amplitude of the air-fuel ratio is uniquely controlled. This has been an obstruction to the realization of the early activation of the catalyst.
In addition to the object of the catalyst activation, also in a case where the response of an air-fuel ratio sensor is detected and a deterioration judgment is made from the detected response, the air-fuel ratio is oscillated between a rich side and a lean side. In such a case, it is desired to oscillate the air-fuel ratio excellently without causing the deterioration of drivability or the like.